There are various problems about lubricating oil compositions due to recent environmental concerns or the like. In particular, there are problems such as prolongation of the life (long drain intervals) of a lubricating oil composition and reduction of specific components (mainly phosphorus atoms) in the lubricating oil composition. The long drain intervals of a lubricating oil composition and reduction of its specific components have been promoted because the long drain intervals are aimed at more efficient use of resources, and reduction of specific components is aimed at safe and economical disposal of a lubricating oil, or in the case where the composition is used as an engine oil, the protection of exhaust gas catalysts is aimed at.
For the long drain intervals of the lubricating oil composition and reduction of its specific components, it is most important to improve the antioxidant ability of the lubricating oil. In particular, lubricating oils such as engine oil or the like may be degraded by heat, moisture, nitric oxide gas or the like, and hence it is essential to improve the antioxidant ability to attain the long drain intervals of the lubricating oil. Therefore, to improve the ability by known antioxidants, the amount of the antioxidant added should then be increased. However, the compound most frequently used as an antioxidant for a lubricating oil is zinc dithiophosphate. Zinc dithiophosphate contains zinc atoms as metals and phosphorus atoms, and it was impossible to reduce the metals or phosphorus atom when the antioxidant (zinc dithiophosphate) was used in larger amounts. Antioxidants such as phenol- and amine-based antioxidants contain no metals and phosphorus atoms, but increases in the addition amounts of the antioxidants cause sludge, etc., so it was impossible to increase the amounts of the antioxidants more than predetermined amount, and the two purposes, the long drain intervals and reduction of specific components such as metals and phosphorus atoms, have not been simultaneously achieved until now.
To solve the problems, various antioxidants have been studied. For example, Patent Document 1 discloses an antioxidant for a lubricant including a styrenated diphenylamine-based compound containing compounds represented by the following formulae (I) and (II) in a total amount of not less than 60 wt %.

Patent Document 2 discloses an antioxidant composition wherein said composition remains in a liquid state even at 0° C. for at least 1 week, which includes 30 to 90% by weight of 2,4-dimethyl-6-t-butyl phenol and 10 to 70% by weight of an alkyl phenol represented by the formula (I):
where R1 and R2 are the same or different and represent hydrocarbon groups having 1 to 18 carbon atoms, X represents at least one kind of a bonding part or a substituent selected from the group consisting of hydrocarbon groups having 1 to 22 carbon atoms, which may contain at least one kind of nitrogen, oxygen, sulfur, and halogen atoms, ester-bond, amide-bond, and sulfide-bond containing groups, m and m′ are the same or different and are each 1 or 2, n and n′ are the same or different and are each 0 or an integer of 1 to 5, and s, t, and u are the same or different and are each 0 or an integer of 1 to 5, but at least two of them do not represent 0 at the same time.
Further, Patent Document 3 discloses a lubricating composition containing, as essential components, an oil-soluble molybdenum compound obtained by reacting one or two or more hexavalent molybdenum compounds selected from molybdenum trioxide, molybdic acid, and alkali salts thereof with a monophosphate or a diphosphate, and a sulfur-containing compound.
Further, Patent Document 4 discloses a lubricating composition containing, as essential components, an oil-soluble molybdenum compound obtained by reacting one or two or more compounds selected from molybdenum trioxide, molybdic acid, and alkali salts thereof with a reducing agent, and then reacting the resultant compound with a monophosphate or a diphosphate; and a sulfur-containing compound.    Patent Document 1: JP 9-53087 A    Patent Document 2: JP 2004-83868 A    Patent Document 3: JP 62-43491 A    Patent Document 4: JP 62-39696 A